This proceedings volume convenes works within the field of fractional calculus and its applications, presented at the International Conference on Fractional Differentiation and its Applications (ICFCA), held in Sousse, Tunisia, from December 26th to 30th, 2024. In its first rendition, the ICFCA gathers papers from several countries such as Algeria, Lebanon, Qatar, Tunisia, Türkiye, and United Arab Emirates, among others. It aims to provide a unique platform for researchers engaged in fractional calculus in a mathematical context. Covered topics range from foundational aspects, such as fractional differential equations, stability analysis, boundary value problems, and inverse problems, to more applied aspects such as fractional control systems, and the use of fractional calculus tools and techniques in physics, engineering, biology, and more. This volume fills a gap in the fractional calculus landscape by covering theoretical developments and applications in various fields while showcasing the recent findings of a new generation of researchers.